Suppose a park is located $3.6$ miles east of your home. The library is 4.8 miles north of the park. What is the shortest distance between your home and the library?

Point B is plotted on the coordinate plane above the $x$-axis. $\triangle B D E$ is equilateral. What are the coordinates of point B to the nearest hundredth?

Javier is standing near a tree. He holds an electronic tape measure near his eyes and finds the three distances shown.

Javier says that he can now use the Pythagorean Theorem to find the height of the tree. Explain. Use vocabulary terms in your explanation.

Glen found the length of the hypotenuse of a right triangle using $\sqrt{a^2+b^2}$. Gigi used $\sqrt{(a+b)^2}$. Who is correct? Explain.

A stainless steel patio heater is shaped like a square pyramid. The length of one side of the base is 19.8 inches. The slant height is 92.8 inches. What is the height of the heater? Round to the nearest tenth of an inch.

The green triangle is set inside a rectangle. Is the green triangle a right triangle? Explain.

Use the Pythagorean Theorem to find the unknown side length of the right triangle.

Determine the length of the longest piece of timber which could be stored in a rectangular shed 8 m by 5 m by 3 m high.

Felipe is making triangles for a stained glass window. He made the design shown, but wants to change it. Felipe wants to move the purple triangle to the corner. The purple piece has side lengths of 4.5 inches, 6 inches, and 7 inches. Can the purple piece be moved to the corner? Explain.

What is the length of side $a$ rounded to the nearest tenth of a centimeter?

Determine the square root.

$$\sqrt{225}$$

During a chemistry experiment, Sam records how the temperature changes over time using ordered pairs (time in minutes, temperature in $^{\circ} \mathrm{C}$). (0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100). Is the relation a function? Explain.

What is the measurement of the longest line segment in a right rectangular prism that is 16 centimeters long, 9 centimeters wide, and 7 centimeters tall? Round to the nearest tenth of a centimeter.

Taylor has tracked the number of students in his grade since third grade. He records his data in the table below. Is the relation a function? Explain. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { Grade } & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { # People } & 726 & 759 & 748 & 792 & 804 & 835 \\ \hline \end{array} $$